Many Requirements

AtCoder

IDabc165_c

Time2000ms

Memory256MB

Difficulty—

Given are positive integers $N$, $M$, $Q$, and $Q$ quadruples of integers ( $a_i$ , $b_i$ , $c_i$ , $d_i$ ). Consider a sequence $A$ satisfying the following conditions: * $A$ is a sequence of $N$ positive integers. * $1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M$. Let us define a score of this sequence as follows: * The score is the sum of $d_i$ over all indices $i$ such that $A_{b_i} - A_{a_i} = c_i$. (If there is no such $i$, the score is $0$.) Find the maximum possible score of $A$. ## Constraints * All values in input are integers. * $2 ≤ N ≤ 10$ * $1 \leq M \leq 10$ * $1 \leq Q \leq 50$ * $1 \leq a_i < b_i \leq N$ ( $i = 1, 2, ..., Q$ ) * $0 \leq c_i \leq M - 1$ ( $i = 1, 2, ..., Q$ ) * $(a_i, b_i, c_i) \neq (a_j, b_j, c_j)$ (where $i \neq j$) * $1 \leq d_i \leq 10^5$ ( $i = 1, 2, ..., Q$ ) ## Input Input is given from Standard Input in the following format: $N$ $M$ $Q$ $a_1$ $b_1$ $c_1$ $d_1$ $:$ $a_Q$ $b_Q$ $c_Q$ $d_Q$ [samples]

Samples

Input #1

Output #1

110

When $A = {1, 3, 4}$, its score is $110$. Under these conditions, no sequence has a score greater than $110$, so the answer is $110$.

Input #2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Output #2

Input #3

10 10 1
1 10 9 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Many Requirements",
    "description": {
      "content": "Given are positive integers $N$, $M$, $Q$, and $Q$ quadruples of integers ( $a_i$ , $b_i$ , $c_i$ , $d_i$ ). Consider a sequence $A$ satisfying the following conditions: *   $A$ is a sequence of $N$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc165_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are positive integers $N$, $M$, $Q$, and $Q$ quadruples of integers ( $a_i$ , $b_i$ , $c_i$ , $d_i$ ).\nConsider a sequence $A$ satisfying the following conditions:\n\n*   $A$ is a sequence of $N$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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